I'm not sure Hitler is getting very old. His health was hetting poor in '45 in OTL. If he secures a victory that he considers satisfying in 1940, he'll probably fare a bit better, but he's not fated to become very old, I think. fter his death, it'll become increasingly clear that turning France and Poland into depopulated regions was a dumb move, and Germany's isolation will have increasingly unpleasant economic repercussions.
I think that by this time (say, late '50s?) Germany will have atomic weapons, thus preventing invasion, but its prospects will actually be dim. They have to either denazify themselves and edge their way back into the international system, or they can double down and proclaim themselves the "only pure" country, pretending that their paranoid isolation is a deliberate choice.
And let's be appropriately cynical here. First off, while murdering millions of Jews and Eastern Europeans is horrible, you know that the Anglo-Americans are going to care a whole lot more when it's millions of Western Europeans being industrially slaughtered. So "denazifying" is going to have to be very convincing and thorough before Germany is treated as a regular peer nation again... something which the Nazi leadership may not be willing to do. Beyond that, the Nazis are a bunch of rabid assholes, and while the Soviets managed de-Stalinisation, I think it's in the Nazi character to always choose "double down" instead of "back down".
For these reasons, I see this victorious Reich slipping into a North Korea-like status, which is why Italy (along with Spain and the rest of Southern Europe) would feel the powerful urge to back away to relative safrty, all while making no sudden moves...